Bi-directional Earthquake Excitations Research Articles

Shake-table testing of a self-centering precast reinforced concrete frame with shear walls

The seismic performance of a self-centering precast reinforced concrete (RC) frame with shear walls was investigated in this paper. The lateral force resistance was provided by self-centering precast RC shear walls (SPCW), which utilize a combination of unbonded prestressed post-tensioned (PT) tendons and mild steel reinforcing bars for flexural resistance across base joints. The structures concentrated deformations at the bottom joints and the unbonded PT tendons provided the self-centering restoring force. A 1/3-scale model of a five-story self-centering RC frame with shear walls was designed and tested on a shake-table under a series of bi-directional earthquake excitations with increasing intensity. The acceleration response, roof displacement, inter-story drifts, residual drifts, shear force ratios, hysteresis curves, and local behaviour of the test specimen were analysed and evaluated. The results demonstrated that seismic performance of the test specimen was satisfactory in the plane of the shear wall; however, the structure sustained inter-story drift levels up to 2.45%. Negligible residual drifts were recorded after all applied earthquake excitations. Based on the shake-table test results, it is feasible to apply and popularize a self-centering precast RC frame with shear walls as a structural system in seismic regions.

A mixed explicit–implicit time integration approach for nonlinear analysis of base-isolated structures

The paper investigates the accuracy, the stability and the computational efficiency of a mixed explicit–implicit time integration approach proposed for predicting the nonlinear response of base-isolated structures subjected to earthquake excitation. Adopting the central difference method for evaluating the response of the nonlinear base isolation system and the Newmark’s constant average acceleration method for estimating the superstructure linear response, the proposed partitioned solution approach is used to analyze a 3D seismically isolated structure subjected to a bidirectional earthquake excitation. Both isolation systems adopting lead rubber and friction pendulum bearings are considered. Numerical results show that the computational time required by the proposed method, in spite of its conditional stability arising from the use of the central difference method in the explicit integration substep, is clearly reduced in comparison to the widely used implicit time integration method adopted in conjunction with the pseudo-force approach (i.e., pseudo-force method). As a matter of fact, the typical low stiffness of the isolation system leads to a critical time step larger than the one used to define the ground acceleration accurately and the proposed method preserves its computational efficiency even in the case of isolators with very high initial stiffness (i.e., friction pendulum bearings) for which the critical time step size could become smaller.

Seismic response of two-way asymmetric building installed with hybrid arrangement of dampers under bi-directional excitations

This article presents a comparative study of the linearly elastic, single-storey, two-way asymmetric system under bi-directional earthquake excitation. The comparative study includes the following dampers: linear and nonlinear fluid viscous dampers, semi-active friction damper and hybrid arrangement of fluid viscous dampers and semi-active friction damper. The response is obtained by numerically solving the governing equations of motion using state space method. The effect of power law coefficient, supplemental damping ratio, stiffness coefficient and gain multiplier on peak response which includes lateral, torsional displacement and acceleration are investigated. To study the effectiveness of dampers, the controlled response of asymmetric system is compared with the corresponding uncontrolled response. The parametric study indicated that the hybrid arrangement of damper is quite effective in reducing various responses. It is further observed that fluid viscous dampers are effective in reducing displacement response and semi-active friction dampers are effective in reducing acceleration response.

Seismic response of two-way asymmetric building installed with hybrid arrangement of dampers under bi-directional excitations

This article presents a comparative study of the linearly elastic, single-storey, two-way asymmetric system under bi-directional earthquake excitation. The comparative study includes the following dampers: linear and nonlinear fluid viscous dampers, semi-active friction damper and hybrid arrangement of fluid viscous dampers and semi-active friction damper. The response is obtained by numerically solving the governing equations of motion using state space method. The effect of power law coefficient, supplemental damping ratio, stiffness coefficient and gain multiplier on peak response which includes lateral, torsional displacement and acceleration are investigated. To study the effectiveness of dampers, the controlled response of asymmetric system is compared with the corresponding uncontrolled response. The parametric study indicated that the hybrid arrangement of damper is quite effective in reducing various responses. It is further observed that fluid viscous dampers are effective in reducing displacement response and semi-active friction dampers are effective in reducing acceleration response.

Energy Spectra of Constant Ductility Factors for Orthogonal Bidirectional Earthquake Excitations

Current research findings about energy spectra are almost entirely based on the single-degree of freedom system that is only fit for two dimensional analyses. Therefore, it is necessary to establish energy spectra of multidimensional systems subjected to multidirectional earthquake excitations. The bidirectional energy balance equation is established based on the single-mass bi-degrees of freedom system. The equation of normalized energy spectra is presented with earthquake motions, periods, and strength reduction factors as variables. The approximate relation of strength reduction factors between the x and y directions are derived from the seismic influence coefficient spectra. The 89 pairs of bidirectional earthquake motion records are selected as earthquake excitations to establish mean normalized input energy spectra and hysteretic energy spectra. The spectral values of normalized energy are compared between the single-mass bi-degrees of freedom system and single degree of freedom system, which shows that in some cases traditional energy spectra may underestimate the energy responses. The influence factors of mean spectra such as period, ductility factor, period ratio, and soil site are analyzed. Analytic results show that the coupling influences of nonlinear responses of structural two lateral components are considered in normalized energy spectra and are theoretically more rational than traditional spectra. In addition, two kinds of energy spectra have the typical spectral pattern features of the soil site, while the pattern and values of the two kinds of spectra are affected by the ductility factor, period ratio and the soil site.

Extending modal pushover-based scaling procedure for nonlinear response history analysis of multi-story unsymmetric-plan buildings

The modal-pushover-based-scaling (MPS) procedure has been developed for appositely selecting and scaling earthquake records for nonlinear response history analyses (RHAs) of multi-story symmetric-plan and single-story unsymmetric-plan buildings. This procedure is extended here to unsymmetric-plan buildings with significant torsional response under bi-directional earthquake excitations. The accuracy of the procedure is evaluated by using three-dimensional computer models of nine unsymmetric-plan buildings with 5, 10 and 15 stories. These models were subjected to nonlinear RHAs considering sets of seven far-field records selected and scaled according to the extended modal-pushover-based-scaling (EMPS) procedure. Structural responses were compared against benchmark values, defined as the median values of the engineering demand parameters (EDPs) due to a larger set of unscaled far-field records. Also examined here is the ASCE/SEI 7-10 scaling procedure for comparison purposes. This study clearly shows that the EMPS procedure provides much superior results in terms of accuracy (true estimates of expected median EDPs) and efficiency (reduced record-to-record variability of EDPs) than the ASCE/SEI 7-10 scaling procedure for far-field ground motions. Thus, the EMPS is deemed to be an appropriate procedure for nonlinear RHAs of multi-story unsymmetric-plan buildings.

Exploring Seismic Response of Bridges with Bidirectional Coupled Modelling of Base Isolation Bearings System

Special bridges, curved, skew and long-span bridges need particular attentions in their analysis, modelling, seismic design, and construction to maintain structures performance at earthquake exposure up to the expectations. Typically, these bridges exhibit complex behaviour in which the flexural and torsional vibration motions are strongly coupled that promotes much solicitude about their behaviours under environmental dynamic loads such as earthquake. Application of passive control system has been shown to be effective to protect bridges under seismic excitation. The accurate description of the shear force deformation responses of the base isolation bearings under bidirectional earthquake excitation loading is major for analysis and design of base-isolated bridges since the using un-coupled modelling approach with two separate unidirectional models could not accurately describe the bidirectional coupled behaviour of the isolation bearing. A simplified lumped mass model of target bridges is used to investigate the seismic response under bidirectional excitation either harmonic or real earthquake ground motions; the Bouc–Wen model is used to capture coupling feature of the shear force deformation behaviour. The seismic response demands of the bridge model with bidirectional interaction modelling approach are compared with those without interaction. Numerical results show that the isolated bridge is significantly influenced by the bidirectional interaction of bearing forces.

Assessment of spectrum matching procedure for nonlinear analysis of symmetric- and asymmetric-plan buildings

Current performance-based seismic design procedures rely on response history analysis (RHA) for estimating engineering demand parameters (EDPs) of base-isolated structures, high-rise buildings and irregular structural systems. Ground motion records for RHAs should be appositely selected in compliance with site-specific hazard conditions, and properly modified either by amplitude-scaling or spectrum matching (SM) to ensure that the modified records provide accurate and efficient estimates of “expected” median demands. While amplitude-scaling techniques change intensity of the ground motion record, SM methods also alter the record’s waveform (in frequency or time domain) to match its response spectrum to a target (or design) spectrum. The research on adequacy of spectrum-matched records for nonlinear RHAs of buildings is not only limited to symmetric-plan buildings subjected to one component of ground motion but also lacks consensus. This study comprehensively examines the accuracy and efficiency of a SM method for nonlinear RHAs under bi-directional earthquake excitations by covering single- and multi-story buildings having symmetric- and asymmetric-plans. For this evaluation, three-dimensional computer models of 48 single-story and nine multi-story buildings were created. Their structural responses were obtained from subsets of seven records modified by SM and separately by amplitude-scaling according to the regulatory ASCE/SEI 7-10 scaling procedure. The accuracy and efficiency of both procedures are examined by comparing their median EDP estimates from subset of records against the median values of EDPs due to a larger set of unscaled records, and by comparing record-to-record variability of the response. It is shown that the time-domain SM procedure provides more accurate median EDP estimates as compared to the ASCE/SEI 7-10 amplitude scaling procedure; however, it critically vanishes the variability of EDPs associated with aleatoric uncertainty in ground motion records. Retaining a certain level of aleatoric variability in EDPs can be an important parameter to be considered for certain projects.

Dynamic responses of two buildings connected by viscoelastic dampers under bidirectional earthquake excitations

In this study, dynamic responses of two buildings connected by viscoelastic dampers under bidirectional excitations are extensively investigated. The two buildings are a 10-story building and a 16-story building, with the shorter building on the left. Viscoelastic dampers are installed at all floors of the shorter building. Equations of motion are formulated using a fractional derivative model to represent the viscoelastic dampers. Three cases are considered with mass eccentricities at 0, 10% and −10% with respect to the dimensions of the buildings. The responses of the buildings are numerically predicted at different damper properties. The simulation results indicated that the maximum horizontal responses of the buildings without eccentricities are significantly mitigated. However, torsional effects are adversely increased. For asymmetric buildings, the effectiveness of the connecting dampers is affected by building eccentricities. As a result, mass eccentricities must be taken into account in damper selection. When compared with vibrations induced by unidirectional excitations, bidirectional excitations can increase the responses of coupled asymmetric buildings. In addition, installing dampers only at the top floor of the shorter building may cause a sudden change in lateral stiffness of the taller building. Consequently, the story shear envelopes of the taller building are changed.

An improved multidimensional MPA procedure for bidirectional earthquake excitations.

Presently, the modal pushover analysis procedure is extended to multidimensional analysis of structures subjected to multidimensional earthquake excitations. an improved multidimensional modal pushover analysis (IMMPA) method is presented in the paper in order to estimate the response demands of structures subjected to bidirectional earthquake excitations, in which the unidirectional earthquake excitation applied on equivalent SDOF system is replaced by the direct superposition of two components earthquake excitations, and independent analysis in each direction is not required and the application of simplified superposition formulas is avoided. The strength reduction factor spectra based on superposition of earthquake excitations are discussed and compared with the traditional strength reduction factor spectra. The step-by-step procedure is proposed to estimate seismic demands of structures. Two examples are implemented to verify the accuracy of the method, and the results of the examples show that (1) the IMMPA method can be used to estimate the responses of structure subjected to bidirectional earthquake excitations. (2) Along with increase of peak of earthquake acceleration, structural response deviation estimated with the IMMPA method may also increase. (3) Along with increase of the number of total floors of structures, structural response deviation estimated with the IMMPA method may also increase.

Experimental study of hollow rectangular bridge column performance under vertical and cyclically bilateral loads

To investigate the seismic performance of hollow reinforced concrete (RC) bridge columns of rectangular cross section under constant axial load and cyclically biaxial bending, five specimens were tested. A parametric study is carried out for different axial load ratios, longitudinal reinforcement ratios and lateral reinforcement ratios. The experimental results showed that all tested specimens failed in the flexural failure mode and their ultimate performance was dominated by flexural capacity, which is represented by the rupture/buckling of tensile longitudinal rebars at the bottom of the bridge columns. Biaxial force and displacement hysteresis loops showed significant stiffness and strength degradations, and the pinching effect and coupling interaction effect of both directions severely decrease the structural seismic resistance. However, the measured ductility coefficient varying from 3.5 to 5.7 and the equivalent viscous damping ratio varying from 0.19 and 0.26 can meet the requirements of the seismic design. The hollow RC rectangular bridge columns with configurations of lateral reinforcement in this study have excellent performance under bidirectional earthquake excitations, and may be considered as a substitute for current hollow RC rectangular section configurations described in the Guideline for Seismic Design of Highway Bridges (JTG/T B02-01-2008). The length of the plastic hinge region was found to approach one sixth of the hollow RC rectangular bridge column height for all specimen columns, and it was much less than those specified in the current JTG/T. Thus, the length of the plastic hinge region is more concentrated for RC rectangular hollow bridge columns.

Lead core heating in lead rubber bearings subjected to bidirectional ground motion excitations in various soil types

SUMMARYThis paper investigates the response of lead rubber bearings (LRBs) under bidirectional earthquake excitations when lead core heating effect is of concern. For this purpose, a series of nonlinear response history analyses were conducted with a bilinear force‐deformation relation for LRBs. In the considered bilinear representation, the strength of LRBs deteriorates because of lead core heating under cyclic motions. Response of LRBs was studied in terms of maximum isolator displacements (MIDs) and maximum lead core temperature as a function of isolator characteristics (characteristic strength to weight ratio, Q/W, and post‐yield isolation period, T). Nonlinear response history analyses were performed using two sets of ground motions clustered according to their soil classifications. To quantify the interacted effects of coupled analysis and lead core heating on MID, unidirectional analyses were also performed. Furthermore, the efficacy of equivalent lateral force procedure in estimating the MID of LRBs was also tested for the cases in which temperature‐dependent behavior of LRBs was considered. The results demonstrate that the temperature rises in the lead core of LRBs in bidirectional analyses are approximately 50% higher than that of unidirectional ones. It decreases with increasing Q/W ratio and T. It is also revealed that equivalent lateral force procedure gives close estimations for MID with some overestimation even for temperature‐dependent behavior of LRBs. Copyright © 2013 John Wiley & Sons, Ltd.

Dynamic Analyses of Isolated Structures under Bi-Directional Excitations of Near-Field Ground Motions

Nonlinear response history analyses (NRHA) of a 3-story isolated reinforced concrete (RC) building are carried out under both uni- and bi-directional earthquake excitations of near-field records. NRHA are conducted for a wide range of yield strength (Q/W) of lead rubber bearings (LRB), and isolation period (T). Selected near-field records are used to investigate both the contribution of orthogonal components on maximum isolator displacements and accuracy of equivalent lateral force (ELF) procedure on estimation of maximum isolator displacements. Analyses results show that both the contribution of orthogonal components and accuracy of ELF procedure depend on the soil condition where isolation system is implemented.

Dynamic Analyses of Isolated Structures under Bi-Directional Excitations of Near-Field Ground Motions

Nonlinear response history analyses (NRHA) of a 3-story isolated reinforced concrete (RC) building are carried out under both uni- and bi-directional earthquake excitations of near-field records. NRHA are conducted for a wide range of yield strength (Q/W) of lead rubber bearings (LRB), and isolation period (T). Selected near-field records are used to investigate both the contribution of orthogonal components on maximum isolator displacements and accuracy of equivalent lateral force (ELF) procedure on estimation of maximum isolator displacements. Analyses results show that both the contribution of orthogonal components and accuracy of ELF procedure depend on the soil condition where isolation system is implemented.

Point-to-Surface Pounding of Highway Bridges with Deck Rotation Subjected to Bi-Directional Earthquake Excitations

Post-earthquake survey of several strong earthquakes demonstrated that pounding between the neighboring civil infrastructures, such as building and highway bridge, would induce significant structural damage, even collapse, of the structures. This article presents a pounding experiment of highway bridge, especially focused on the point-to-surface pounding of bridge decks due to torsional rotation, when subjected to extreme bi-directional earthquake excitations. To experimentally investigate the point-to-surface pounding between the neighboring bridge segments, a base-isolated highway bridge model, in which the mass centers of the bridge decks do not strictly coincide with the corresponding stiffness centers, is manufactured. A series of shaking table tests of the highway bridge model are carried out for the structural model with large and small separations of the expansion joint to investigate the dynamic responses of the bridge model with and without including the pounding effects, respectively. An analytical model of the highway bridge, in which the point-to-surface pounding is represented by using a modified contact-friction element, is also established based on the lump mass model with three degrees of freedom for each segment. Based on the test results, the model parameters of the modified contact-friction element are identified, and the analytical responses of the highway bridge model with pounding effects are compared with the experimental data. The results show that the highway bridge is vulnerable to the deck rotation, and point-to-surface pounding should be considered in the structural design to lighten the pounding damage of the highway bridge under strong earthquake excitations.

Seismic behavior of bidirectional-resistant ductile end diaphragms with buckling restrained braces in straight steel bridges

The ductile end diaphragm concept developed for regular (i.e., straight) slab-on-girder or deck-truss steel bridge superstructures is expanded to make it applicable to bidirectional earthquake excitation. Buckling restrained braces (BRBs) are used as the ductile fuses. Two retrofit schemes (Retrofit Scheme-1 and Retrofit Scheme-2) are investigated to seek the best geometrical layout to maximize the dissipated hysteretic energy of the ductile diaphragms with BRB end diaphragms. Closed form solutions are presented for practical design purposes. Behavioral characteristics (strength, stiffness, and drift) of the proposed retrofit schemes for end diaphragms are quantified with an emphasis on hysteretic energy dissipation. Results from selected numerical examples show that the generic bridge geometry, bidirectional loading, and the loading ratio (or the assumed combination rule), have a pronounced effect on the end diaphragm’s inelastic behavior. Volumetric hysteretic energy dissipation is used to compare the effectiveness of the proposed retrofit schemes under several loading cases. These indicate that, in most cases, Retrofit Scheme-1 is superior to Retrofit Scheme-2 and may exhibit better seismic response.

The structural performance of monolithic intersecting walls in a tall reinforced concrete building

AbstractResults of the seismic performance assessment of a new structural system that has been used in a 54‐story reinforced concrete building are presented. The structure, which is still under construction, and has a ‘Y‐shape’ form, utilizes a special structural system that does not include any beams or columns. Instead, walls and slabs are used for carrying both gravitational and lateral loads. The general distinctions of the system are discussed. The structural efficiency of the system is compared with other conventional systems in some existing tall buildings. The seismic responses and dynamic behavior of the structure that were achieved by conducting various analyses are presented. The effects of analysis method, as well as some other parameters such as modeling assumptions and bidirectional earthquake excitation on the linear responses, are studied. The influence of the number of modes and design spectrum on the spectral analysis results is discussed. Using dynamic analysis, the real heightwise distribution of lateral loads occurring during an earthquake is presented. Copyright © 2007 John Wiley & Sons, Ltd.

Influence of soil–structure interaction on the response of seismically isolated cable-stayed bridge

Soil conditions have a great deal to do with damage to structures during earthquakes. This paper attempts to assess the influence of dynamic soil–structure interaction (SSI) on the behavior of seismically isolated cable-stayed bridge supported on a rigidly capped vertical pile groups, which pass through moderately deep, layered soil overlying rigid bedrock. In the present approach, piles closely grouped together beneath the towers are viewed as a single equivalent upright beam. The soil–pile interaction is idealized as a beam on nonlinear Winkler foundation using continuously distributed hysteretic springs and viscous dashpots placed in parallel. The hysteretic behavior of soil springs is idealized using Bouc–Wen model. The cable-stayed bridge is isolated by using high-damping rubber bearings and the effects of SSI are investigated by performing seismic analysis in time domain using direct integration method. The seismic response of the isolated cable-stayed bridge with SSI is obtained under bi-directional earthquake excitations (i.e. two horizontal components acting simultaneously) considering different soil flexibilities. The emphasis has been placed on assessing the significance of nonlinear behavior of soil that affects the response of the system and identify the circumstances under which it is necessary to include the SSI effects in the design of seismically isolated bridges. It is observed that the soil surrounding the piles has significant effects on the response of the isolated bridge and the bearing displacements may be underestimated if the SSI effects are ignored. Inclusion of SSI is found essential for effective design of seismically isolated cable-stayed bridge, specifically when the towers are very much rigid and the soil condition is soft to medium. Further, it is found that the linear soil model does not lead to accurate prediction of tower base shear response, and nonlinear soil modeling is essential to reflect dynamic behavior of the soil–pile system properly.

Seismic Response of Isolated Bridges

The response of bridges seismically isolated by lead-rubber bearings (L-RB) to bidirectional earthquake excitation (i.e., 2 horizontal components) is presented. The force-deformation behavior of L-RB is considered as bilinear, and the interaction between the restoring forces in 2 orthogonal horizontal directions is duly considered in the response analysis. The specific purpose of the study is to assess the effects of seismic isolation on the peak response of the bridges, and to investigate the effects of the bidirectional interaction of restoring forces of isolation bearings. The seismic response of the lumped mass model of continuous span isolated bridges is obtained by solving the governing equations of motion in the incremental form using an iterative step-by-step method. To study the effectiveness of L-RB, the seismic response of isolated bridges is compared with the response of corresponding nonisolated bridges (i.e., bridges without isolation devices). A comparison of the response of the isolated bridges obtained by considering and ignoring the bidirectional interaction of bearing forces is made under important parametric variation. The important parameters included are the flexibility of bridge piers and the stiffness and yield strength of the L-RB. Results show the bidirectional interaction of the restoring forces of the L-RB has considerable effects on the seismic response of isolated bridges. If these interaction effects are ignored, then the peak bearing displacements are underestimated which can be crucial from a design point of view.

Non-linear seismic response of base-isolated liquid storage tanks to bi-directional excitation

Seismic response of the liquid storage tanks isolated by lead-rubber bearings is investigated for bi-directional earthquake excitation (i.e. two horizontal components). The biaxial force-deformation behaviour of the bearings is considered as bi-linear modelled by coupled non-linear differential equations. The continuous liquid mass of the tank is modelled as lumped masses known as convective mass, impulsive mass and rigid mass. The corresponding stiffness associated with these lumped masses has been worked out depending upon the properties of the tank wall and liquid mass. Since the force-deformation behaviour of the bearings is non-linear, as a result, the seismic response is obtained by the Newmark's step-by-step method. The seismic responses of two types of the isolated tanks (i.e. slender and broad) are investigated under several recorded earthquake ground to study the effects of bi-directional interaction. Further, a parametric study is also carried out to study the effects of important system parameters on the effectiveness of seismic isolation for liquid storage tanks. The various important parameters considered are: (i) the period of isolation, (ii) the damping of isolation bearings and (iii) the yield strength level of the bearings. It has been observed that the seismic response of isolated tank is found to be insensitive to interaction effect of the bearing forces. Further, there exists an optimum value of isolation damping for which the base shear in the tank attains the minimum value. Therefore, increasing the bearing damping beyond a certain value may decrease the bearing and sloshing displacements but it may increase the base shear.